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For electromagnetic (EM) scattering by dense media, the traditional approach is to use particles of spheres or ellipsoids that are densely and randomly packed in a background medium. The particles have discrete permittivities that are different from the background medium. The dense-medium model has been applied to the microwave remote sensing of terrestrial snow. In this paper, we propose a different approach of using a bicontinuous medium with discrete permittivities and study the EM scattering properties using analytical and numerical methods. The bicontinuous medium is a continuous representation of interfaces between inhomogeneities within the medium. Discrete permittivities are then assigned to the inhomogeneities of the structure. The analytical approach is based on the Born approximation using the derived analytical correlation functions. The numerical method is based on the numerical Maxwell model of 3-D (NMM3D) approach. In particular, the discrete-dipole approximation and the conjugate gradient-squared method accelerated by the fast Fourier transform technique are used in solving the volume integral equation. Scattering results of analytical and numerical approaches are compared. Numerical results are illustrated using parameters in microwave remote sensing of terrestrial snow. In the NMM3D simulations, three kinds of convergence tests are conducted, viz., convergence with respect to the discretization size, convergence with respect to the sample size, and convergence with respect to the number of realization. The NMM3D results indicate that the scattering by the bicontinuous medium with a broader size distribution has a weaker frequency dependence than that by the medium with a more narrow size distribution. The frequency-dependence power law index can be lower than two, which is very much lower than the power of four in Rayleigh scattering. The NMM3D results also exhibit fairly large cross-polarization returns which account for the local nonisotropic mic- - rostructures of bicontinuous media, although the medium is statistically isotropic.